Figure REF  shows an instantaneous visualization of the spheroid \(\mbox{\textit {Fr}}=2\)  wake in the center-vertical and center-horizontal planes. One of the distinctive features of the spheroid wake is that at \(\mbox{\textit {Fr}}\sim O(1)\)  the separation of the boundary layer can be strongly modulated by the steady lee waves [1]}. This interaction between the lee waves and the wake is particularly strong when the Froude number is close to a critical Froude number \(\mbox{\textit {Fr}}_c=AR/\pi \) , where \(AR\)  is the body aspect ratio. When \(\mbox{\textit {Fr}}\approx \mbox{\textit {Fr}}_c\) , half the wavelength of the lee wave (\(\lambda /D=2\pi \mbox{\textit {Fr}}\) ) coincides with the length of the body and the size of the separation region is reduced. The flow is then in what is called resonant or saturated lee wave regime, [2]}, [3]}. At low Reynolds numbers, this effect can lead to the relaminarization of the turbulent wake [4]}, [1]}. In the present case, figure REF (a) reveals that, even at \(Re=10^5\) , the wake height is strongly modulated by the waves, although the wake is not relaminarized due to the high \(\)  of the flow. For example, the wake height exhibits oscillations with a wavelength of \(\lambda /D= 2\pi \mbox{\textit {Fr}}= 4\pi \) . The modulation of the wake by the waves leads to an unusual configuration in the intermediate wake (\(x=20-40\) ) where the wake width \(L_H\)  is smaller than the wake height \(L_V\) , figure REF (a) and (c). In these figures, sinuous oscillations are observed only in the horizontal plane (figure REF d) due to strong stratification. These horizontal sinuous instabilities contrast with the lee wave induced varicose modulation in the vertical plane. As the wake evolves, the \(L_H < L_V\)  configuration transitions to the expected \(L_H > L_V\) . In this late region, the small-scale turbulence of the boundary layer has been dissipated and a layered-layer structure is observed in the vertical plane, figure REF (b). The qualitative trends of \(L_H\)  and \(L_V\)  discussed here are quantified in §.
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